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← JEE Main 2022 · 28 Jun · Shift 1
MathematicsInteger+4 / -1Question 21 of 90

JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 21

Let R1R_1 and R2R_2 be relations on the set {1,2,…,50}\{1,2,\dots,50\} such that

R1={(p,pn):p is a prime and n≥0 is an integer}R_1=\left\{\left(p,p^n\right):p\text{ is a prime and }n\ge0\text{ is an integer}\right\} and

R2={(p,pn):p is a prime and n=0 or 1}R_2=\left\{\left(p,p^n\right):p\text{ is a prime and }n=0\text{ or }1\right\}.

Then, the number of elements in R1−R2R_1-R_2 is ______.

Answer and worked solution

Official answer: 8

R1−R2R_1-R_2 holds (p,pn)(p,p^n) with n≥2n\ge2 and pn≤50p^n\le50: 4,8,16,324,8,16,32; 9,279,27; 2525; 4949.

Answer: 8

Topics:Relations